Approach to fault detection of time-delay systems using functional observers

A new methodology is reported for designing functional observers to detect actuator faults of a class of time-delay systems where the matrix pair (A, C) is not observable. First, a generalised state transformation is used to transform the system into new coordinates where the delay term associated with the state vector is injected into the system's output and input. Then, a minimum-order functional observer is designed to construct a residual function that can trigger system faults. The finding is significant as it is now possible to detect faults of time-delay systems where the pair (A, C) is not required to be observable. A numerical example is given to illustrate the effectiveness of the proposed design approach. © The Institution of Engineering and Technology 2014.

Partial state estimation for linear systems with output and input time delays.

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.

Scalable approximating SVD algorithm for recommender systems

With the rapid development of Internet, the amount of information on the Web grows explosively, people often feel puzzled and helpless in finding and getting the information they really need. For overcoming this problem, recommender systems such as singular value decomposition (SVD) method help users finding relevant information, products or services by providing personalized recommendations based on their profiles. SVD is a powerful technique for dimensionality reduction. However, due to its expensive computational requirements and weak performance for large sparse matrices, it has been considered inappropriate for practical applications involving massive data. Thus, to extract information in which the user is interested from a massive amount of data, we propose a personalized recommendation algorithm which is called ApproSVD algorithm based on approximating SVD in this paper. The trick behind our algorithm is to sample some rows of a user-item matrix, rescale each row by an appropriate factor to form a relatively smaller matrix, and then reduce the dimensionality of the smaller matrix. Finally, we present an empirical study to compare the prediction accuracy of our proposed algorithm with that of Drineas's LINEARTIMESVD algorithm and the standard SVD algorithm on MovieLens dataset and Flixster dataset, and show that our method has the best prediction quality. Furthermore, in order to show the superiority of the ApproSVD algorithm, we also conduct an empirical study to compare the prediction accuracy and running time between ApproSVD algorithm and incremental SVD algorithm on MovieLens dataset and Flixster dataset, and demonstrate that our proposed method has better performance overall.

Separating spatially correlated signals using first-order precoders

This paper deals with blind separation of spatially correlated signals mixed by an instantaneous system. Taking advantage of the fact that the source signals are accessible in some man-made systems such as wireless communication systems, we preprocess the source signals in transmitters by a set of properly designed first-order precoders and then the coded signals are transmitted. At the receiving side, information about the precoders are utilized to perform signal separation. Compared with the existing precoder-based methods, the new method only employs the simplest first-order precoders, which reduces the delay in data transmission and is easier to implement in practical applications.

A new monotonicity index for fuzzy rule-based systems

A search in the literature reveals that mathematical conditions (usually sufficient conditions) for the Fuzzy Inference System (FIS) models to satisfy the monotonicity property have been developed. A monotonically-ordered fuzzy rule base is important to maintain the monotonicity property of an FIS. However, it may difficult to obtain a monotonically-ordered fuzzy rule base in practice. We have previously introduced the idea of fuzzy rule relabeling to tackle this problem. In this paper, we further propose a monotonicity index for the FIS system, which serves as a metric to indicate the degree of a fuzzy rule base fulfilling the monotonicity property. The index is useful to provide an indication whether a fuzzy rule base should (or should not) be used in practice, even with fuzzy rule relabeling. To illustrate the idea, the zero-order Sugeno FIS model is exemplified. We add noise as errors into the fuzzy rule base to formulate a set of non-monotone fuzzy rules. As such, the metric also acts as a measure of noise in the fuzzy rule base. The results show that the proposed metric is useful to indicate the degree of a fuzzy rule base fulfilling the monotonicity property.

Ordinal random fields for recommender systems

Recommender Systems heavily rely on numerical preferences, whereas the importance of ordinal preferences has only been recognised in recent works of Ordinal Matrix Factorisation (OMF). Although the OMF can effectively exploit ordinal properties, it captures only the higher-order interactions among users and items, without considering the localised interactions properly. This paper employs Markov Random Fields (MRF) to investigate the localised interactions, and proposes a unified model called Ordinal Random Fields (ORF) to take advantages of both the representational power of the MRF and the ease of modelling ordinal preferences by the OMF. Experimental result on public datasets demonstrates that the proposed ORF model can capture both types of interactions, resulting in improved recommendation accuracy.

Soft tissue characterisation using a force feedback-enabled instrument for robotic assisted minimally invasive surgery systems

An automated laparoscopic instrument capable of non-invasivemeasurement of tip/tissue interaction forces for direct application in robotic assisted minimally invasive surgery systems is introduced in this chapter. It has the capability to measure normal grasping forces as well as lateral interaction forces without any sensor mounted on the tip jaws. Further to non-invasive actuation of the tip, the proposed instrument is also able to change the grasping direction during surgical operation. Modular design of the instrument allows conversion between surgical modalities (e.g., grasping, cutting, and dissecting). The main focus of thispaper is on evaluation of the grasping force capability of the proposed instrument. The mathematical formulation of fenestrated insert is presented and its non-linear behaviour is studied. In order to measure the stiffness of soft tissues, a device was developed that is also described in this chapter. Tissue characterisation experiments were conducted and results are presented and analysed here. The experimental results verify the capability of the proposed instrument in accurately measuring grasping forces and in characterising artificial tissue samples of varying stiffness.

A new algorithm to design minimal multi-functional observers for linear systems

Designing minimum possible order (minimal) observers for Multi-Input Multi-Output (MIMO) linear systems have always been an interesting subject. In this paper, a new methodology to design minimal multi-functional observers for Linear Time-Invariant (LTI) systems is proposed. The approach is applicable, and it also helps in regulating the convergence rate of the observed functions. It is assumed that the system is functional observable or functional detectable, which is less conservative than assuming the observability or detectability of the system. To satisfy the minimality of the observer, a recursive algorithm is provided that increases the order of the observer by appending the minimum required auxiliary functions to the desired functions that are going to be estimated. The algorithm increases the number of functions such that the necessary and sufficient conditions for the existence of a functional observer are satisfied. Moreover, a new methodology to solve the observer design interconnected equations is elaborated. Our new algorithm has advantages with regard to the other available methods in designing minimal order functional observers. Specifically, it is compared with the most common schemes, which are transformation based. Using numerical examples it is shown that under special circumstances, the conventional methods have some drawbacks. The problem partly lies in the lack of sufficient numerical degrees of freedom proposed by the conventional methods. It is shown that our proposed algorithm can resolve this issue. A recursive algorithm is also proposed to summarize the observer design procedure. Several numerical examples and simulation results illustrate the efficacy, superiority and different aspects of the theoretical findings.

Global finite-time stabilisation for a class of stochastic nonlinear systems by output feedback

In this paper, the problem of global finite-time stabilisation by output feedback is considered for a class of stochastic nonlinear systems. First, based on homogeneous systems theory and the adding a power integrator technique, a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system. Then, the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms; it is shown that the proposed output-feedback control law can guarantee that the closed-loop system is global finite-time stable in probability. Finally, simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme.

A functional observer based fault detection technique for dynamical systems

This paper presents a functional observer based fault detection method. The fault detection is achieved using a functional observer based fault indicator that asymptotically converges to a fault indicator that can be derived based on the nominal system. The asymptotic value of the proposed fault indicator is independent of the functional observer parameters and also the convergence rate of the fault indicator can be altered by choosing appropriate functional observer parameters. The advantage of using this new method is that the observed system is not necessarily needed to be observable; therefore, the proposed fault detection technique is also applicable for systems where state observers cannot be designed; moreover, the functional observer fault detection scheme is always of reduced order in comparison to a state observer based scheme.

New results in common functional state estimation for two linear systems with unknown inputs

This paper presents new developments in common functional observers for two systems. We improve an existing common functional observer scheme by reducing its order, and then investigate its existence conditions in terms of the original system matrices. These conditions have never been explored and they enable the users to know at the outset the class of systems for which the scheme is applicable. They also show that both observers can be designed independently of each other which significantly simplifies the design process. A numerical simulation verifies the findings.

Design of state observers for interconnected time-delay systems via a coordinate transformation approach

This paper considers the design of state observers for interconnected time-delay systems using a coordinate transformation method. Through such a transformation, the system that has interconnection and state delays is metamorphosed into a new system that injects time-delay information into its input and output terms, before reintroducing them back into the latter system, effectively coupling the delay terms into the IO injection terms and eliminating the delay values from the state variables. Next, full-order and reduced-order observers are designed based on the transformed system. Finally, the observed states of the transformed system that correspond to the original system is used to deduce the estimates of the original system. A numerical example is provided of an interconnected time-delay system.

Nonlinear backstepping controller design for sharing active and reactive power in three-phase grid-connected photovoltaic systems

In this paper, a nonlinear backstepping controller is designed for three-phase grid-connected solar photovoltaic (PV) systems to share active and reactive power. A cascaded control structure is considered for the purpose of sharing appropriate amount of power. In this cascaded control structure, the dc-link voltage controller is designed for balancing the power flow within the system and the current controller is designed to shape the grid current into a pure sinusoidal waveform. In order to balance the power flow, it is always essential to maintain a constant voltage across the dc-link capacitor for which an incremental conductance (IC) method is used in this paper. This approach also ensures the operation of solar PV arrays at the maximum power point (MPP) under rapidly changing atmospheric conditions. The proposed current controller is designed to guarantee the current injection into the grid in such a way that the system operates at a power factor other than unity which is essential for sharing active and reactive power. The performance of the proposed backstepping approach is verified on a three-phase grid-connected PV system under different atmospheric conditions. Simulation results show the effectiveness of the proposed control scheme in terms of achieving desired control objectives.

Haptic technology for micro-robotic cell injection training systems — a review

Currently, the micro-robotic cell injection procedure is performed manually by expert human bio-operators. In order to be proficient at the task, lengthy and expensive dedicated training is required. As such, effective specialized training systems for this procedure can prove highly beneficial. This paper presents a comprehensive review of haptic technology relevant to cell injection training and discusses the feasibility of developing such training systems, providing researchers with an inclusive resource enabling the application of the presented approaches, or extension and advancement of the work. A brief explanation of cell injection and the challenges associated with the procedure are first presented. Important skills, such as accuracy, trajectory, speed and applied force, which need to be mastered by the bio-operator in order to achieve successful injection, are then discussed. Then an overview of various types of haptic feedback, devices and approaches is presented. This is followed by discussion on the approaches to cell modeling. Discussion of the application of haptics to skills training across various fields and haptically-enabled virtual training systems evaluation are then presented. Finally, given the findings of the review, this paper concludes that a haptically-enabled virtual cell injection training system is feasible and recommendations are made to developers of such systems.

A delay-dependent functional observer for linear time-invariant systems with input delay

A delay-dependent functional observer is designed for linear time-invariant (LTI) systems with time-varying input delay. Compared to delay-free observers, delay-dependent functional observers are less conservative and cover more systems. The designed functional observer is with minimum possible order (minimal). Necessary and sufficient conditions of the existence of the observer and asymptomatic stability of it are illustrated. The proposed observer is extended to multiple input delayed systems with time-varying delays. An algorithm is developed for designing of the minimal order observer based on the methodology of this paper. Two numerical examples and simulations are used to support our proposed methodology.